Does the Introductory Physics Course Cover Too Much?

Some of the bigger ideas in the first part of the introductory physics course. Rhett Allain

I’m currently in the middle of a summer section of introductory physics – the algebra based version. I’ve come to the realization that perhaps we expect too much from the students. My typical summary of the first semester of intro physics is something like this:

The great thing about physics is that we can build many things based on a few fundamental ideas. Really, in this course there are only three big ideas. These ideas are:

The momentum principle. This says that a net force changes the momentum of an object. Typically, textbooks choose to write this as “Newton’s Second Law” – but really I think we should just call this the momentum principle.

Work Energy Principle. The work done on a system is equal to the change in energy of the system.

Angular Momentum Principle. The net torque on an object is equal to the change in angular momentum (time rate of change of angular momentum).

That’s pretty much the whole first semester. Sure, you could add fluids and pressure or you could add sound and waves – but I think that’s too much. In fact, I think the above three ideas are too much.

Why is this too much? Let’s start with something like kinematics. Kinematics isn’t one of these three big ideas, but it is a building block for the momentum principle. In kinematics, students look at the relationship between position, velocity and acceleration. There are several stumbling blocks here. Let’s start with a few:

Vectors. In an algebra-based physics course, very few (if any) of the students have seen a vector before. However, they need to not only learn about vectors, they need to actually use them. Wait! There’s more! How can you understand vectors if you are rusty on your trigonometry? Trust me. Many of these students need some help in this area too. I guess it’s obvious that students NEED vectors to comprehend kinematics.

Rate of change. Acceleration is the time rate of change of velocity (change in velocity divided by change in time). This seems simple, but it really isn’t. Just look at how many students (after instruction) say that if you toss a ball in the air, the acceleration is zero at the highest point. There is a basic confusion between a thing at that thing’s rate of change.

Graphs. You don’t HAVE to use graphs in kinematics, but it is very common. Students come in with many difficulties interpreting graphs. My favorite question shows the position as a function of time for two trains. One train is moving at a constant speed and one train starts out from rest and accelerates to catch the other train. When asked about the speed when the two curves cross, many students say they have the same position AND speed at that point. Yes, this is partially a problem with rate of change and partially a problem with graphs.

The point is that even with the very first concept in introductory physics, there are many things that students must not only understand but master in order to progress. Learning physics isn’t like building a pyramid with introductory concepts at the bottom. No. Learning physics is like an upside down pyramid that gets bigger at the top. All of this mass at the top of the pyramid is being supported by these initial ideas. A small crack in these supporting ideas will bring down the whole thing.

What should we do to make it better?

Well, there is another question we should ask first. Why are students taking introductory physics? In particular, why are they taking this algebra-based physics? If you ask the students, just about all of them would say “because it’s required for my major.” Other students might say that it’s not required but they need to do well on the MCAT to get into medical school. And here is the problem.

In almost all cases, the algebra-based physics course isn’t something that the physics department decides how to build. The course content in these physics courses are usually determined by the requirements of the biology major and other departments that need this course for their students. I guess that we could at least remove any extra material from the course. I know biologist want to include pressure – but maybe this could be removed.

What about in an ideal world? What if we could rebuild the course from scratch with no constraints? I think the initial question should still be “why are students taking this course?” I would hope the answer would be that they are taking this to have an understanding of physics in the same way that they should understand art or history (because these are the things that make us human).

If you want an intro-physics course for humans (without external requirements), I would say it should have the following:

Exploration of the historical development of some physics models. For instance, a critical look at the whole Aristotle-Galileo-Newton force vs. motion thing.

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